Determination of the charge transfer when tunneling into putative Majorana modes in individual vortices in FeTe$_{0.55}$Se$_{0.45}$

In iron-based superconductors, vortices are reported to host elusive Majorana bound states, but the evidence for their presence remains controversial. Local shot noise measurements have been suggested as a probe into vortex physics, but despite much theoretical work, no local measurement of the shot noise of a vortex core exists. Here, we use local shot-noise spectroscopy to study the tunneling process into vortex bound states for the first time, both in the conventional superconductor NbSe$_2$ and in the putative Majorana platform FeTe$_{0.55}$Se$_{0.45}$. We find that tunneling into vortex bound states in both cases exhibits charge transfer of a single electron charge. Our data for the zero-energy bound states in FeTe$_{0.55}$Se$_{0.45}$ excludes the possibility of Yu-Shiba-Rusinov states and is consistent with Majorana bound states. However, it is also consistent with trivial vortex bound states--we argue that further theoretical investigations taking into account dynamics and superconducting tips are necessary.